Une condition suffisante pour l’irréductibilité d’une induite parabolique de {\rm GL}(m,{\rm D})

Badulescu, Ioan; Lapid, Erez; Mínguez, Alberto

doi:10.5802/aif.2828

Cited by 13 publications

(14 citation statements)

References 9 publications

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“…Irreducibility is part of Theorem 3.9 of the paper [BLM13] due to Badulescu et al , which gives a sufficient condition for a product to be irreducible: when no segment of is juxtaposed (in the obvious sense) to a segment in .…”

Section: Local Conjecture Formentioning

confidence: 99%

Branching laws for classical groups: the non-tempered case

Gan¹,

Gross²,

Prasad

2020

Compositio Math.

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This paper generalizes the Gan–Gross–Prasad (GGP) conjectures that were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the non-generic L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of Arthur parameters that governs the branching laws for ${{\rm GL}}_n$ and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in Gan et al. [Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I, Astérisque 346 (2012), 1–109] including Bessel models and Fourier–Jacobi models.

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Section: Local Conjecture Formentioning

confidence: 99%

Branching laws for classical groups: the non-tempered case

Gan¹,

Gross²,

Prasad

2020

Compositio Math.

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“…In Section 7, we prove a criterion for irreducibility of a product of the form Zp∆qˆLp∆ 1 q where ∆ 1 has length 2. This is a modular version of a result known in the complex case (Theorem 3.1 in [3]). We begin Section 8 with some basic results on H-distinguished representations of G. The first tool is to use Lemma 8.8, the conditions that we get from the three orbits that we mentioned above.…”

Section: 8mentioning

confidence: 51%

Modular representations of GL(n) distinguished by GL(n-1) over a p-adic field

Sécherre

Venketasubramanian

2015

Preprint

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Let F be a non-Archimedean locally compact field, q be the cardinality of its residue field, and R be an algebraically closed field of characteristic ℓ not dividing q. We classify all irreducible smooth R-representations of GLnpFq having a nonzero GLn´1pFq-invariant linear form, when q is not congruent to 1 mod ℓ. Partial results in the case when q is 1 mod ℓ show that, unlike the complex case, the space of GLn´1pFq-invariant linear forms has dimension 2 for certain irreducible representations.

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“…Remark 6.4. A. Mínguez has explained us how to get in a simple way the above proposition from Lemma 1.2 of [4] (providing in this way a proof in terms of Jacquet modules). The case when one representation is cuspidal follows from [13].…”

Section: Now the Condition Of Inclusion Of Underlying Sets Tells Us Imentioning

confidence: 99%

“…C. Jantzen's numerous corrections helped us a lot to improve the style of the paper. A. Mínguez has explained us how to get alternative proof based on Jacquet modules of the main result of section 6 (by simple use of Lemma 1.2 from [4]; see Remark 6.4 of this paper for a few more details). We are thankful to all them.…”

Section: Introductionmentioning

confidence: 99%

Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,𝒜))

Tadić

2014

Glas. Mat. Ser. III

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Let A be a finite dimensional central division algebra over a local nonarchimedean field F . Fix any parabolic subgroup P of GL(n, A) and a Levi factor M of P . Let π be an irreducible unitary representation of M and ϕ a (not necessarily unitary) character of M . We give an explicit necessary and sufficient condition for the parabolically induced representation Ind GL(n,A) P (ϕπ) to be irreducible.

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Une condition suffisante pour l’irréductibilité d’une induite parabolique de {\rm GL}(m,{\rm D})

Cited by 13 publications

References 9 publications

Branching laws for classical groups: the non-tempered case

Branching laws for classical groups: the non-tempered case

Modular representations of GL(n) distinguished by GL(n-1) over a p-adic field

Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,𝒜))

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